On-shell supersymmetry breaking in the Abelian Chern-Simons-matter model in three dimensions of spacetime

This study examines on-shell supersymmetry breaking in the Abelian $\mathcal{N}=1$ Chern-Simons-matter model within a three-dimensional spacetime. The classical Lagrangian is scale-invariant, but two-loop radiative corrections to the effective potential break this symmetry, along with gauge and on-shell supersymmetry. To investigate this issue, the Renormalization Group Equation is used to calculate the two-loop effective potential.